I am gonnaing to talk about my favourite movie named Three Idiots, which is a famous Indian movie by a renowned director.

"gonna" is a rather casual word that you usually only see in speech, and it doesn't fit in with the level of formality in the rest of this entry.

After this movie was relaxed out, it became an immediate box-office hit, playing to full houses worldwide.

I have watched this movie three times, but it has never failed to fascinate me.

Grammatically you weren't wrong, but "it never failed to fascinate me" comes across as more of an objective statement, where as because you use "but", I expect you to say something a bit more emotive about how much you like the movie. I think any of the below three would be fine:
1. I have watched this movie three times, and it never failed to fascinate me. (More objective tone)
2. I have watched this movie three times, but it has never failed to fascinate me. (More emotive, but with a very very slight implication that it could fail to fascinate you in the future).
3. I have watched this movie three times, but it never fails to fascinate me. (More emotive, without the implication in example 2).

This movie talkeds about the lives of the three male leads.

At that time in India, people believed that only if one can become the top of his class and ace every test, can he find a decent job in his later life, especially in engineering.

This sentence largely sounds "technically correct" to me, but poorly/somewhat unnaturally worded. I'd personally rewrite it as

"At that time in India, people believed that, especially in engineering, someone can only find a decent job later in life by being the top of his class and acing every test."

One of the things that fascinates me most about this movie is that it is really transformative and educational, whichand has revolutionised the way people think.

The reason why I die forom this movie is that it tells us that parents should not make every decision for their children.

"die from" = the movie causes you to die
"die for" = you like the movie a lot

Every walk of life deserves our engagement.,

Sso we should support our children and respect them.

Starting a sentence with "So" is a bit awkward, it'd be better to combine this with the previous sentence.

The main characters in this movie always do some stupid and funny things to make people burst out ofin laughter.

I am gonnawill talk about my favourite movie named Three Idiots, which is a famous Indian movie by a renowned director.

Maybe this is pedantic, but if you say "favorite movie named Three Idiots", it implies there are multiple movies named "Three Idiots", and one of them is your favorite.

After this movie was relaxed outeased, it became an immediate box-office hit, playscreening to full houses worldwide.

I feel like "screening" is more precise than "playing"

I have watched this movie three times, butand it never faileds to fascinate me.

This movie talkeds about the lives of the three male leads.

Saying "three male leads" (without the "the") implies there are more than three male leads, but the movie only talks about three of them. This is unlikely correct.

At that time in India, people believed that only if one cane is required to become the top of histheir class and ace every test, can he in order to find a decent job in his later life, especially in engineering.

English seems to be moving away from using the male pronoun "he" for a singular person of unknown gender. I've used "singular they" above.

The "only if..., can he..." grammar construct is feels overloaded here, and I'd discourage its use in general. I'm guessing it's used here because it's equivalent to 只要……才能…… in Chinese. But it's hard for the reader/listener to parse these sentences, and therefore (in my opinion) better to rephrase.

In this casTherefore, parents want their children to perform well in academia, and don’t allow their children to develop their hobbies like sport ands or photography.

One of the things that fascinates me most about this movie is that it is really transformative and educational, whichand has revolutionised the way people think.

Be aware that "revolutionised" (rather than "-ized") is the typical spelling in British English.

The reason why I die from this movie is that it tells uI feel the moral of the story is that parents should not make every decision for their children.

"why I die from this movie" this sounds like the movie literally kills you. I don't know what this is meant to mean, so I changed it to something I would normally expect.

Every walk of life deserves our engagementis worthy of our appreciation.

I don't think we necessarily need to "engage" with every "walk of life" (is this even possible?), we just need to "respect" and "appreciate" it.

So we should support and respect our children and respect them.

Maybe we will be amazed by their crowing achieveeventual accomplishments in the domain they areir areas of interested in.

It's spelled "crow[n]ing achievement", but the use of this term here feel forced (what if they don't have a "crowning achievement" in later life? It's quite unusual.); "accomplishments" sounds more accurate, and I added "eventual" since achievements are not immediately obtained.

I'm a bit reluctant to consider "sports" etc. a "domain".

On top of thatMoreover, this movie is really funny.

"On top of that" is correct, but wordy.

The main characters in this movie always do somerepeatedly do stupid and funny things to makecausing people to burst out of laughtering.

Here "repeatedly" is more precise than "always".

Here "people" should be more precise: does it refer to the audience or the other actors in the movie?